{
  "id": "2110.06343",
  "version": "v2",
  "published": "2021-10-12T20:41:06.000Z",
  "updated": "2022-08-01T20:02:00.000Z",
  "title": "Equivalence of Fell bundles is an equivalence relation",
  "authors": [
    "Anna Duwenig",
    "Boyu Li"
  ],
  "comment": "42 pages",
  "categories": [
    "math.OA",
    "math.FA"
  ],
  "abstract": "We introduce the notion of groupoid pre-equivalences and prove that they give rise to groupoid equivalences by taking certain quotients. Then, given an equivalence of Fell bundles $\\mathscr{B}$ and $\\mathscr{C}$ and another equivalence between $\\mathscr{C}$ and $\\mathscr{D}$, we construct an equivalence between $\\mathscr{B}$ and $\\mathscr{D}$ out of the tensor product bundle. As a consequence, we obtain that Fell bundle equivalence is indeed an equivalence relation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-08-01T20:02:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L55",
      "46L05",
      "22A22"
    ],
    "keywords": [
      "equivalence relation",
      "fell bundle equivalence",
      "tensor product bundle",
      "groupoid equivalences",
      "groupoid pre-equivalences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}